When depth-converted seismic horizon data are available, the geomodeler must consider how to integrate the data into the model. He must create horizon surfaces which respect both the seismic interpretation and the well markers. Even when all the wells, with or without sonic, are used for time-to-depth conversion, it is rare that the seismic interpretation matches precisely to the well markers. The reasons are many. The velocity maps might not have respected exactly the velocity value at each well. The time-depth conversion itself, once the velocity is modeled, might not have been exact either. This is not as rare as one might think. The reason might be also a question of timing in the team. Some well locations or some well KB elevation might have been adjusted after the depth-conversion was done. Similarly, the geologist might have modified slightly the markers interpretation after the velocity maps were completed. At last, some wells might have been drilled after the seismic data got depth-converted. Or it might be a combination of all these events. In a perfect world, the geophysicist would systematically redo the depth-conversion. But in many projects, the team might not have the time for that. The geophysicist might have been already assigned to some other tasks (or projects)...or the final deadline for the whole project might be too close to provide an opportunity to redo the depth-conversion.

If the mismatches are large, it is still recommended to adjust the velocity model and redo the depth-conversion. But if mismatches are reasonable, then they can be fixed directly in the geomodeling package. The technique, described hereafter, can probably be applied in many geophysical packages.
In Figure 1A, a seismic interpretation (blue line) has been depth-converted using the three wells 1, 2 and 3. The interpreted horizon is close to the well markers but a mismatch remains. Should it be corrected? A general rule in geomodeling is that if well data and seismic data are partly in contradiction, the well data shall be respected in priority because well data are more precise than seismic data. In the process of adjusting to the well, we try to respect the seismic data as much as possible. Naturally, if well and seismic data are in complete contradiction, it is wiser to understand ‘why’ instead of enforcing this rule blindly. Once the source of the inconsistency is identified, the team might agree that the data can be corrected to make them coherent one with the other, or the team might decide that the inconsistency is the result of different interpretations (for example). In that case, several geomodels might be needed, one for each interpretation. For the purposes of this section, we assume that it makes sense for our dataset to modify the seismic horizon to fit to the well markers.
One might be tempted to simply create a surface from the seismic interpretation and then adjust this map directly to the markers. By doing this, we mean using the depth of each marker to adjust the depth of the map. Such an approach might be risky. While the markers will be respected, it is also very likely that the whole surface will be completely smoothed out even far from the wells. The adjusted map might look very similar to the map we could generate from the markers alone. If it happens, at the least the team needs to decide if that was the intention or if a different approach is needed. Creating a map showing the difference between the original and the corrected geometry is a nice way to understand how the geomodeling process modified the map exactly.

Instead of interpolating the depth values directly, we suggest another approach which better respects the geometry of the seismic interpretation: create a map of the adjustment you need to apply to the seismic horizon map (Figure 1A, blue line) to get it to fit to the markers. Then move the seismic horizon map with this adjustment map.

The first step of this workflow is to compute the mismatch between the original seismic map and each well marker. In our example (Figure 1A), the mismatch at well 1 is +1.2m, the mismatch at well 2 is +0.9m and the mismatch at well 3 is -0.6m. A negative number means that the marker is deeper than the surface at this location. We now know that the adjustment map must have the value +1.2, +0.9 and ‑0.6 at the respective XY locations of wells 1, 2 and 3 (Figure 1B). We also decide that the adjustment must be null past a certain distance from each well location. It means that outside of areas centered at each well, we don’t want to modify the original seismic map.

The second step of this workflow is to define the radius of these areas. More details will be given in a later paragraph. Once the radius defined, we know the displacement at each well and we know the displacement is 0m beyond the radius. All that remains to do is to use some interpolation technique to extrapolate a decreasing displacement from each well toward the limit of its associated area. On Figure 1B, it is illustrated by a bell shape around each well. Lastly, the displacement map is added to the original seismic horizon. The resulting, corrected horizon is equal to the original map far from the wells (= outside of the pre-defined radial zones around each wells) while the horizon has now changed around each well. Each marker is now respected while keeping the overall geometry of the seismic interpretation.

As illustrated in Figure 2, the challenge is to decide what radius to use around each well. In this example, the mismatch at well A is half of the mismatch at well B. If we use a very small radius for both wells (Figure 2A, black thin line), the adjustment zone is really narrow and the corrected horizon surfaces might show an obvious bullseye around each well. Using a medium-size radius (Figure 2A, red dashed line), the bullseye effect might be less noticeable, and so acceptable, around well A, while it might still be too visible around well B. At last, using a large radius (Figure 2A, green thick line), the bullseye effect might now be minimal on both wells, but the question might become that we are altering a too large portion of the seismic maps around each well.

Ultimately, this is all a trade-off that the team must agree upon. If some mismatches are really too large or the bullseyes are too visible, then, as mentioned earlier, it might be wiser to redo the depth-conversion. An alternate approach might be to use different radii for each well (Figure 2B). The idea is to select a radius proportional to the absolute value of the mismatch: the more important the mismatch, the larger the radius. In Figure 2B, we could use a medium radius around well A and a large one around well B.

Once surfaces are created for each horizon on the well markers and a seismic interpretation exists, the geomodeler can continue taking advantage of the seismic interpretation in two ways, both illustrated in Figure 3.

Figure 3 is an extension of the example presented in Figure 2. Horizon A is the one for which a seismic interpretation existed, and got adjusted to the well markers at wells 1, 2 and 3. For the horizons B and C though, there is no seismic interpretation, only well markers.

In many reservoirs the horizons, or a subset of them, might be conformable, one with the other. If one of these conformable horizons has been picked on seismic, then it can be used as a reference to model the other horizons. In Figure 3, Horizon B is interpreted as conformable with Horizon A. We can use the geometry of the Horizon A to model the geometry of Horizon B. A thickness map of the unit between Horizon A and Horizon B is interpolated from the thickness at each well (using geostatistical algorithms). Then, the geometry of Horizon B is calculated by subtracting the thickness map to the depth map of Horizon A. This is a first additional way to take advantage of a seismic interpretation. Sometimes, none of the seismic events they can interpret correspond to any of the stratigraphic markers interpreted by the geologists on the wells. These events are linked to other change of log signatures along the wells. When this happens, it is recommended to treat such horizon as we did here with Horizon A, and then create horizons for the real stratigraphic tops (= the horizons we do need for the 3D-grid) following the approach proposed here for Horizon B.

Other horizons known only from well markers are simply not conformable to any horizon picked on seismic. Such horizons can only be modeled from the well markers. No seismic horizon, such as Horizon A, can be used as a reference. In Figure 3, this is the case of Horizon C.

Another use of seismic interpretations is for quantifying the uncertainty on the geometry of the horizons. Horizons A, B and C illustrate different type of uncertainty geomodelers have to consider.

Horizon A is the best defined horizon as it was visible on seismic. There are still two sources of uncertainty though: uncertainty in the picking itself in the time domain and uncertainty in the depth-conversion (or depth migration as discussed at the beginning of the previous section).

Horizon B was created from Horizon A. As such, it inherits all Horizon A’s sources of uncertainty. An additional uncertainty must be considered too: the uncertainty on the thickness of the unit between Horizon A and Horizon B.

Horizon C, at last, is only known from well markers. As such, we have no real idea of how uncertain the interpolated surface is. Of course, mathematically, we can run different scenarios for this horizon, but which scenario bound to the uncertainty shall we use? +/- 5m? +/- 50m? More maybe? A solution is to define the range of uncertainty on Horizon C from Horizon A with the following approach.

Firstly, we create a new surface for Horizon A only from well markers. Such geometry is illustrated in a dashed blue line on Figure 3. We now have two geometries for Horizon A: the surface made from the seismic and the well markers and the geometry made only from the well markers. The mismatch between the two maps tells us how incorrect – that is to say how uncertain – our map of Horizon A from the markers alone is. On Figure 3, the error is reasonable between the wells (yellow color), while it is very large to the east beyond well 3. One might assume that a similar range of uncertainty would have been found around Horizon C if it would have been possible to pick it on seismic. If we accept this assumption, we can simply assign the uncertainty map from Horizon A onto Horizon C (Figure 3, vertical thick arrows).

Many geomodeling packages have tools to create multiple versions of a given horizon, each version being a variation around a base case geometry. The tool is fed with an initial geometry of the horizon (Figure 3, the interpolated Horizon C map from the well markers) as well as an estimate of the range of uncertainty (Figure 3, the map of mismatches computed on Horizon A). Each variation is slightly different from the reference surface, but all surfaces fall within the range of uncertainty pre-defined by the uncertainty map. In Figure 3, a few possible variations of Horizon C are represented in thin dark lines.

Up to this point, this section focused on integrating “traditional” seismic horizon interpretations. By “traditional”, we mean surfaces that can be picked across the whole seismic cube such as Horizon A on Figure 3. In the last few paragraphs of this section, we are considering the integration of the smaller seismic events that can be picked inside each geological unit.

In geomodeling, once the top and bottom horizons of a reservoir are modeled, we often create a 3D-grid with a mesh parallel to the top horizon, parallel to the base horizon or proportional between the two surfaces. If it seems more appropriate for the local geology, we can instead make the mesh horizontal (Figure 4A) or parallel to a surface other than the top and bottom horizons. In all these approaches, the seismic cube is not used to create the mesh, except when the reference surface the mesh is parallel to was itself picked on seismic.

This being said, as geomodelers, we should not forget that the internal heterogeneity of the reservoir might be partly visible on the seismic, in the form of local seismic events, that geophysicists can pick. A close collaboration between the geologist and the geophysicist might be needed there to ensure that those local, internal seismic events are coherent with the geological interpretation of the reservoir. If such local events are interpreted, it is in the team’s interest to see these local seismic events being used in the construction of the geomodel.

At the time this chapter is written (autumn 2015), geomodeling packages start having tools to take these local events into account when creating the mesh of the 3D-grid. Figure 4B illustrates this concept as the mesh is following a few seismic events picked in the reservoir (thick blue lines between Horizon A and Horizon B). While such techniques are still not widespread, we think geomodelers should already start looking into this. Property modeling in a 3D-grid (facies and petrophysics) is primarily guided by the geometry of the 3D-grid itself. If we can add more “geology” into these meshes by using the local seismic events, we might improve the accuracy of our models.